Shopping could not be completed faster. If blocks were found twice as fast, then it would take 12 blocks for a transaction to confirm, as each block would be worth half as much.
I think if you worked the maths through carefully 12 blocks of half the difficulty would actually be somewhat more secure than 6 blocks at the current difficulty.
Similarly I think that the current scheme is more secure than 3 blocks at twice the difficulty or one block at six times the difficulty.
I think it works a little bit the same way that compound interest using the exponential function is more lucrative than effectively the same rate of simple interest. So 100% simple interest on x after 1 year gives you 2x. 50% interest half-yearly gives 2.25x. 25% quarterly gives 2.44x and the limit is e = 2.7183ish
I don't have time to justify this at the moment. Hopefully I will either revisit this topic or someone else will pick up the torch.
For the practical purposes above, the difference will be small.